After last season's breakthrough and his success in the summer's Club World Cup, Gonzalo has found himself sidelined this season by coach Xabi Alonso.
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As such, a loan move in January has been mooted for the centre-forward.
The Daily Mail says should Real management and Gonzalo agree to the temporary departure, a move to England could be on.
Watching developments are Brighton, but they're not alone with Leeds, Sunderland and Aston Villa also being mentioned as potential destinations.